Finite Group Databasebeta

← #28339480

Subgroups — #28339480

Order 13696.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812082C211yesmaximal, characteristic
2C2×#16812071C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D107C211yesmaximal, characteristic, complemented
6#20292527C211yesmaximal, characteristic, complemented
7#20292522C211yesmaximal, characteristic, complemented
8#20292520C211yesmaximal, characteristic, complemented
9#20292517C211yesmaximal, characteristic, complemented
10#20292505C211yesmaximal, characteristic, complemented
11#20292503C211yesmaximal, characteristic, complemented
12#20292501C211yesmaximal, characteristic, complemented
13#20292478C211yesmaximal, characteristic, complemented
14#20292474C211yesmaximal, characteristic, complemented
15#385×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22C22×C4×D107C2211yescharacteristic
23#16812082C418yescomplemented
24#16812071—24no—
25C4×C22⋊D107—24no—
26C4×C22⋊D107—24no—
27C2×C4⋊Dic107C2211yescharacteristic
28C2×Dic107⋊C4C2211yescharacteristic
29C2×Dic107⋊C4C2211yescharacteristic
30C2×Dic107⋊C4C2211yescharacteristic
31C2×Dic107⋊C4C2211yescharacteristic
32C4⋊C4×D107—24no—
33C2×C22⋊Dic107C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic
39C2×(C2×D107)⋊C4C2211yescharacteristic
40C2×(C2×D107)⋊C4C2211yescharacteristic
41C2×C4×Dic107C2211yescharacteristic
42C2×C4×Dic107C2211yescharacteristic
43C2×C4×Dic107C2211yescharacteristic
44C2×C4×Dic107C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C107⋊#95C2211yescharacteristic
47C107⋊#95C2211yescharacteristic
48C107⋊#95C2211yescharacteristic
49C23×C4×C107C2211yescharacteristic
50C2×C4⋊C4×C107C2211yescharacteristic
51C2×C4⋊C4×C107C2211yescharacteristic
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C22⋊C4×C107C2211yescharacteristic
54#95×C107C2211yescharacteristic
55#95×C107C2211yescharacteristic
56C23×D107C2311yescharacteristic
57C23×D107C2311yescharacteristic
58C2×D428—22no—
59C2×D428—22no—
60C2×D428C2×C414yescomplemented
61C2×C22⋊D107—22no—
62C2×C22⋊D107—22no—
63C2×C22⋊D107—22no—
64C2×C22⋊D107—22no—
65C2×C22⋊D107C2×C414yescomplemented
66C2×C22⋊D107C2×C414yescomplemented
67C22×Dic107C2311yescharacteristic
68C22×Dic107C2311yescharacteristic
69C22×Dic107C2311yescharacteristic
70C22×Dic107C2311yescharacteristic
71C22×Dic107C2311yescharacteristic
72C22×Dic107C2311yescharacteristic
73C2×C4×D107—22no—
74C2×C4×D107—22no—
75C2×C4×D107—22no—
76C2×C4×D107—22no—
77C2×C4×D107—22no—
78C2×C4×D107—22no—
79C2×C4×D107—22no—
80C2×C4×D107—22no—
81C2×C4×D107—41no—
82C2×C4×D107—41no—
83C2×C4×D107—41no—
84C2×C4×D107C2×C414yescomplemented
85C4⋊Dic107—22no—
86Dic107⋊C4—22no—
87Dic107⋊C4—22no—
88Dic107⋊C4C2×C414yescomplemented
89Dic107⋊C4D414yescomplemented
90C22⋊Dic107—22no—
91C22⋊Dic107—22no—
92(C2×D107)⋊C4—22no—
93(C2×D107)⋊C4—22no—
94(C2×D107)⋊C4—22no—
95(C2×D107)⋊C4—41no—
96(C2×D107)⋊C4C2×C414yescomplemented
97(C2×D107)⋊C4D414yescomplemented
98C4×Dic107—22no—
99C4×Dic107—22no—
100C4×Dic107—22no—
101C4×Dic107—22no—
102C24×C107C2311yescharacteristic
103C22×C4×C107—22no—
104C22×C4×C107—22no—
105C22×C4×C107—41no—
106C22×C4×C107C2311yescharacteristic
107C22×C4×C107C2311yescharacteristic
108C22×C4×C107C2311yescharacteristic
109C22×C4×C107C2311yescharacteristic
110C22×C4×C107C2311yescharacteristic
111C22×C4×C107C2311yescharacteristic
112C4⋊C4×C107—22no—
113C4⋊C4×C107—22no—
114C22⋊C4×C107—41no—
115C22⋊C4×C107C2×C414yescomplemented
116C23×C107—21no—
117C23×C107—21no—
118C23×C107—21no—
119C23×C107—21no—
120C23×C107—21no—
121C23×C107—21no—
122C23×C107C22×C412yes—
123C23×C107C2411yescharacteristic
124C22×D107—21no—
125C22×D107—21no—
126C22×D107—21no—
127C22×D107—21no—
128C22×D107—21no—
129C22×D107—21no—
130C22×D107—21no—
131C22×D107—21no—
132C22×D107—21no—
133C22×D107—21no—
134C22×D107C22×C412yes—
135C22×D107C22×C412yes—
136C22×D107C2×D412yes—
137C22×D107#4112yes—
138C2×C4×C107—21no—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—21no—
144C2×C4×C107—21no—
145C2×C4×C107—21no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—21no—
151C2×C4×C107—21no—
152C2×C4×C107—44no—
153C2×C4×C107C22×C412yes—
154C2×C4×C107C22×C412yes—
155C2×C4×C107C2×D412yes—
156C2×C4×C107C2×D412yes—
157C22⋊D107—28no—
158C22⋊D107—28no—
159C2×Dic107—21no—
160C2×Dic107—21no—
161C2×Dic107—21no—
162C2×Dic107—21no—
163C2×Dic107—21no—
164C2×Dic107—21no—
165C2×Dic107—21no—
166C2×Dic107—21no—
167C2×Dic107—21no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107—21no—
171C2×Dic107C22×C412yes—
172C2×Dic107C22×C412yes—
173C2×Dic107C2×D412yes—
174C2×Dic107C2×D412yes—
175C2×Dic107C2×D412yes—
176C2×Dic107#4112yes—
177D428—28no—
178C4×D107—28no—
179C4×D107—44no—
180C4×D107—44no—
181C4×D107—44no—
182C22×C107—22no—
183C22×C107—22no—
184C22×C107—22no—
185C22×C107—41no—
186C22×C107—41no—
187C22×C107—41no—
188C22×C107—41no—
189C22×C107C23×C411yescharacteristic
190C22×C107C22×D411yescharacteristic
191C22×C107C22×D411yescharacteristic
192C22×C107C2×#4111yescharacteristic
193C22×C107C2×#4111yescharacteristic
194C22×C107H(5,𝔽2)11yescharacteristic
195C22×C1072−1+411yescharacteristic
196C2×D107—22no—
197C2×D107—22no—
198C2×D107—22no—
199C2×D107—22no—
200C2×D107—22no—
201C2×D107—22no—
202C2×D107—22no—
203C2×D107—22no—
204C2×D107—22no—
205C2×D107—41no—
206C2×D107—41no—
207C2×D107—41no—
208C2×D107—41no—
209C2×D107C4×D414yescomplemented
210C4×C107—22no—
211C4×C107—22no—
212C4×C107—22no—
213C4×C107—22no—
214C4×C107—41no—
215C4×C107—41no—
216Dic107—22no—
217Dic107—22no—
218Dic107—22no—
219Dic107—41no—
220Dic107—41no—
221Dic107C4×D414yescomplemented
222C2×C107—42no—
223C2×C107C2×C4×D411yescharacteristic
224C2×C107C2×C4×D411yescharacteristic
225C2×C107#52011yescharacteristic
226C2×C107D4211yescharacteristic
227C2×C107#54711yescharacteristic
228C2×C107#54811yescharacteristic
229C2×C107#55311yescharacteristic
230D107—24no—
231D107—42no—
232#2361—1071nomaximal, Sylow
233C107#236111yescharacteristic, complemented, Sylow
234C2×#121—1071no—
235C2×C4×D4—1071no—
236C2×C4×D4—1071no—
237C2×C4×D4—1071no—
238C22×C4⋊C4—1071no—
239#390—1071no—
240#389—1071no—
241#388—1071no—
242#388—1071no—
243#386—1071no—
244#386—1071no—
245#385—1071no—
246#385D10711yescharacteristic, complemented
247C4×C4⋊C4—1071no—
248C4×C22⋊C4—1071no—
249C22×D4—1071no—
250C22×D4—1071no—
251C22×D4—1071no—
252C23×C4—1071no—
253C23×C4—1071no—
254C23×C4—1071no—
255C23×C4—1071no—
256C23×C4C2×D10711yescharacteristic
257#121—1078no—
258C4×D4—2144no—
259C4×D4—2144no—
260C4×D4—2144no—
261C2×C4⋊C4—1071no—
262C2×C4⋊C4—1071no—
263C2×C4⋊C4—1071no—
264C2×C4⋊C4—1071no—
265C2×C4⋊C4—1071no—
266C2×C4⋊C4—2144no—
267C2×C4⋊C4C2×D10711yescharacteristic
268C2×C4⋊C4C2×D10711yescharacteristic
269C2×C22⋊C4—1071no—
270C2×C22⋊C4—1071no—
271C2×C22⋊C4—1071no—
272C2×C22⋊C4—1071no—
273C2×C22⋊C4—1071no—
274C2×C22⋊C4—1071no—
275C2×C22⋊C4—1071no—
276C2×C22⋊C4—1071no—
277C2×C22⋊C4C2×D10711yescharacteristic
278C2×C22⋊C4C2×D10711yescharacteristic
279C2×C42—1071no—
280C2×C42—1071no—
281C2×C42—1071no—
282C2×C42—1071no—
283#95—1071no—
284#95—1071no—
285#95—1071no—
286#95—1071no—
287#95C2×D10711yescharacteristic
288#95C2×D10711yescharacteristic
289C24—1071no—
290C24—1071no—
291C24C22×D10711yescharacteristic
292C2×D4—1074no—
293C2×D4—1074no—
294C2×D4—1074no—
295C2×D4—2142no—
296C2×D4—2142no—
297C2×D4—2142no—
298C2×D4—2142no—
299C2×D4—2142no—
300C2×D4—2142no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—1071no—
305C22×C4—1071no—
306C22×C4—1071no—
307C22×C4—1071no—
308C22×C4—1074no—
309C22×C4—1071no—
310C22×C4—1071no—
311C22×C4—4281no—
312C22×C4—4281no—
313C22×C4—4281no—
314C22×C4—2142no—
315C22×C4—2142no—
316C22×C4—2142no—
317C22×C4—2142no—
318C22×C4—2142no—
319C22×C4—2142no—
320C22×C4—2142no—
321C22×C4—2142no—
322C22×C4C22×D10711yescharacteristic
323C22×C4C22×D10711yescharacteristic
324C22×C4C22×D10711yescharacteristic
325C22×C4C22×D10711yescharacteristic
326C22×C4C22×D10711yescharacteristic
327C22×C4C22×D10711yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—1074no—
331C4⋊C4—1074no—
332C4⋊C4—2142no—
333C4⋊C4—2142no—
334C4⋊C4—2142no—
335C22⋊C4—41no—
336C22⋊C4—1074no—
337C22⋊C4—1074no—
338C22⋊C4—4281no—
339C22⋊C4—2142no—
340C22⋊C4—2142no—
341C22⋊C4—2142no—
342C22⋊C4—2142no—
343C22⋊C4—2142no—
344C22⋊C4C4×D10714yescomplemented
345C42—2142no—
346C42—2142no—
347C42—2142no—
348C42—2142no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—1072no—
356C23—1072no—
357C23—1072no—
358C23—1072no—
359C23—2141no—
360C23—2141no—
361C23—2141no—
362C23—2141no—
363C23—2141no—
364C23—2141no—
365C23—2141no—
366C23—2141no—
367C23—2141no—
368C23—2141no—
369C23C2×C4×D10712yes—
370C23C23×D10711yescharacteristic
371D4—2148no—
372D4—2148no—
373D4—2148no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—44no—
389C2×C4—1072no—
390C2×C4—1072no—
391C2×C4—1072no—
392C2×C4—1072no—
393C2×C4—1072no—
394C2×C4—1072no—
395C2×C4—4284no—
396C2×C4—4284no—
397C2×C4—4284no—
398C2×C4—2148no—
399C2×C4—2141no—
400C2×C4—2141no—
401C2×C4—2141no—
402C2×C4—2141no—
403C2×C4—2141no—
404C2×C4—2141no—
405C2×C4—2141no—
406C2×C4—2141no—
407C2×C4—2141no—
408C2×C4—2141no—
409C2×C4—2141no—
410C2×C4—2141no—
411C2×C4C2×C4×D10712yes—
412C2×C4C2×C4×D10712yes—
413C2×C4D4×D10712yes—
414C2×C4D4×D10712yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—1074no—
423C22—4281no—
424C22—4281no—
425C22—4281no—
426C22—4281no—
427C22—2142no—
428C22—2142no—
429C22—2142no—
430C22—2142no—
431C22—2142no—
432C22—2142no—
433C22—2142no—
434C22—2142no—
435C22—2142no—
436C22C22×C4×D10711yescharacteristic
437C22C2×D4×D10711yescharacteristic
438C22C2×D4×D10711yescharacteristic
439C22#41×D10711yescharacteristic
440C22#41×D10711yescharacteristic
441C22#1681215411yescharacteristic
442C22#1681215711yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—1074no—
450C4—4281no—
451C4—4281no—
452C4—2142no—
453C4—2142no—
454C4—2142no—
455C2—42no—
456C2—4282no—
457C2—2144no—
458C2C4×D4×D10711yescharacteristic
459C2C4×D4×D10711yescharacteristic
460C2#2029310811yescharacteristic
461C2#2029325911yescharacteristic
462C2#2029327911yescharacteristic
463C2#2029328711yescharacteristic
464C2#2029332211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#385×C107C2
socle, cosocleC23×C107C24
prime radicalC2×#16812082C2
hypercenter#385D107
hypocenterC107#2361
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #385

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16812071C2semidirect
3. C2×C4×C22⋊D107C2semidirect
4. C2×C4×C22⋊D107C2semidirect
5. C2×C4⋊C4×D107C2semidirect
6. #20292527C2semidirect
7. #20292522C2semidirect
8. #20292520C2semidirect
9. #20292517C2semidirect
10. #20292505C2semidirect
11. #20292503C2semidirect
12. #20292501C2semidirect
13. #20292478C2semidirect
14. #20292474C2semidirect
15. #385×C107C2semidirect
23. #16812082C4semidirect
60. C2×D428C2×C4semidirect
65. C2×C22⋊D107C2×C4semidirect
66. C2×C22⋊D107C2×C4semidirect
84. C2×C4×D107C2×C4semidirect
88. Dic107⋊C4C2×C4semidirect
89. Dic107⋊C4D4semidirect
96. (C2×D107)⋊C4C2×C4semidirect
97. (C2×D107)⋊C4D4semidirect
115. C22⋊C4×C107C2×C4semidirect
209. C2×D107C4×D4semidirect
221. Dic107C4×D4semidirect
233. C107#2361semidirect
246. #385D107semidirect
344. C22⋊C4C4×D107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168120822
C2×#168120712
C2×C4×C22⋊D1072
C2×C4⋊C4×D1072
#202925272
#202925222
#202925202
#202925172
#202925052
#202925032
#202925012
#202924782
#202924742
#385×C1072
#2361107